Holographic Thermodynamics of Higher-Dimensional AdS Black Holes with CFT Rescaling

TL;DR

The paper addresses how boundary CFT rescaling, captured by the central charge $C$, influences the thermodynamics and phase structure of charged AdS black holes in higher dimensions. It advances CHET by treating the conformal rescaling factor as a thermodynamic parameter with fixed Newton's constant and a varying AdS radius, deriving a nondegenerate first law that includes a $\mu dC$ term and a consistent Smarr relation. The study finds Van der Waals–like critical behavior in $D=5$ and $D=6$, with three regimes determined by $C$: first-order transitions for $C>C_c$, a second-order transition at $C=C_c$, and a single stable phase for $C<C_c$, highlighting the boundary degrees of freedom as key drivers of bulk thermodynamics. These results reinforce the dimensional dependence of holographic thermodynamics and suggest further exploration of rotating solutions and their boundary duals.

Abstract

In this paper, we study the thermodynamic behavior of charged AdS black holes in higher-dimensional spacetimes within the framework of conformal holographic extended thermodynamics. This formalism is based on a novel AdS/CFT dictionary in which the conformal rescaling factor of the boundary conformal field theory (CFT) is treated as a thermodynamic parameter, while Newton's constant is held fixed and the AdS radius is allowed to vary. We explore how variations in the CFT state, represented by its central charge, influence the bulk thermodynamics, phase structure, and stability of black holes in five and six dimensions. Our analysis reveals the emergence of Van der Waals like phase transitions and critical phenomena governed by the central charge. Additionally, we find that the thermodynamic behavior of AdS black holes is affected by the dimensionality of the bulk spacetime, as we compare higher-dimensional black holes to lower-dimensional ones, such as BTZ black holes. These findings provide new insights into the role of boundary degrees of freedom in shaping the thermodynamics of gravitational systems via holography.

Figures (6)

• Figure 1: $T-S$ curves of 5D charged AdS black holes for different states of CFT.
• Figure 2: $F-T$ curves of 5D charged AdS black holes for different states of CFT.
• Figure 3: Heat capacity evolution of 5D charged AdS black holes for different states of CFT.
• Figure 4: $T$–$S$ curves of 6D charged AdS black holes for different states of CFT.
• Figure 5: $F$–$T$ curves of 6D charged AdS black holes for different states of CFT.